DO NOW

1

2

3

DO NOW

1

2

3

# 𝑜𝑓 𝑏𝑢𝑙𝑏𝑠 = 50

# 𝑜𝑓 𝑏𝑢𝑟𝑛𝑒𝑑 𝑜𝑢𝑡 = 8

Boys : Girls4:5

148

Determining Surface Area of Three-

Dimensional Figures Module 5 Lessons 18

Objective 6.G.A.4

SWBAT represent three-dimensional figures

using nets made up of rectangles and triangles

and use the nets to find the surface area of

these figures IOT solve real world and

mathematical problems.

recognize or discover

something that could happen in reality

relating to math

find an answer to

a polygon with three angles and three sides

a quadrilateral with four right angles and two pairs of opposite equal parallel sides

having three dimensions; length, width, and height

a flat shape which can be folded into a three-dimensional solid

the total area of the faces of a three-dimensional solid

be a symbol for

6.G.A.4 Word Wall• Dimension - directions that an object

can be measured

• Net - a flat shape which can be folded into a three-dimensional solid

• Three-dimensional - having three dimensions; length, width, and height

• Triangle - a polygon with three angles and three sides

• Rectangle - a quadrilateral with four right angles and two pairs of opposite equal parallel sides

• Solve - to apply an operation(s) in order to find a value

• Surface area - the total area of the faces of a three-dimensional solid

Rectangular Prism

4𝑖𝑛 × 1𝑖𝑛 = 4𝑖𝑛2

4𝑖𝑛 × 1𝑖𝑛 = 4𝑖𝑛2

4𝑖𝑛 × 2𝑖𝑛 = 8𝑖𝑛2

4𝑖𝑛 × 2𝑖𝑛 = 8𝑖𝑛2

2𝑖𝑛

×1𝑖𝑛

=2𝑖𝑛

2

2𝑖𝑛

×1𝑖𝑛

=2𝑖𝑛

2

To determine surface area, we found the area of each of the faces and then added those areas

𝑆𝐴 = 2 4𝑖𝑛 × 1𝑖𝑛 + 2 4𝑖𝑛 × 2𝑖𝑛 + 2(2𝑖𝑛 × 1𝑖𝑛)

Each part of the expression represents an area of one face of the given figure. We were able to write a more compacted form because there are three pairs of two faces that are identical.

𝑆𝐴 = 2 4𝑖𝑛 × 1𝑖𝑛 + 2 4𝑖𝑛 × 2𝑖𝑛 + 2(2𝑖𝑛 × 1𝑖𝑛)

= 2 4𝑖𝑛2 + 2 8𝑖𝑛2 + 2(2𝑖𝑛2)

= 8𝑖𝑛2 + 16𝑖𝑛2 + (4𝑖𝑛2)

= 28𝑖𝑛2

WE DO

4 𝑖𝑛 × 2 𝑖𝑛 4 𝑖𝑛 × 2 𝑖𝑛 4 𝑖𝑛 × 1 𝑖𝑛 4 𝑖𝑛 × 1 𝑖𝑛 2 𝑖𝑛 × 1 𝑖𝑛 2 𝑖𝑛 × 1 𝑖𝑛

8𝑖𝑛2 2𝑖𝑛22𝑖𝑛24𝑖𝑛24𝑖𝑛28𝑖𝑛2

𝑙 × 𝑤 𝑤 × ℎ𝑤 × ℎ𝑙 × ℎ𝑙 × ℎ𝑙 × 𝑤

𝑆𝐴 = 𝑙 × 𝑤 + 𝑙 × 𝑤 + 𝑙 × ℎ + 𝑙 × ℎ + 𝑤 × ℎ + 𝑤 × ℎ

𝑆𝐴 = 2(𝑙 × 𝑤) + 2(𝑙 × ℎ) + 2(𝑤 × ℎ)Length

Width

Height

I DO

15𝑐𝑚 × 6𝑐𝑚 15𝑐𝑚 × 6𝑐𝑚 15𝑐𝑚 × 8𝑐𝑚 15𝑐𝑚 × 8𝑐𝑚 6𝑐𝑚 × 8𝑐𝑚 6𝑐𝑚 × 8𝑐𝑚

90𝑐𝑚2 48𝑐𝑚248𝑐𝑚2120𝑐𝑚2120𝑐𝑚290𝑐𝑚2

𝑙 × 𝑤 𝑤 × ℎ𝑤 × ℎ𝑙 × ℎ𝑙 × ℎ𝑙 × 𝑤

Length

Width

Height

WE DO

𝑆𝐴 = 2(𝑙 × 𝑤) + 2(𝑙 × ℎ) + 2(𝑤 × ℎ)

𝑆𝐴 = 2(20𝑐𝑚 × 5𝑐𝑚) + 2(20𝑐𝑚 × 9𝑐𝑚) + 2(5𝑐𝑚 × 9𝑐𝑚)

𝑆𝐴 = 2(100𝑐𝑚2) + 2(180𝑐𝑚2) + 2(45𝑐𝑚2)

𝑆𝐴 = 200𝑐𝑚2 + 360𝑐𝑚2 + 90𝑐𝑚2

𝑆𝐴 = 650𝑐𝑚2

Length

Width

HeightI DO

𝑆𝐴 = 2(𝑙 × 𝑤) + 2(𝑙 × ℎ) + 2(𝑤 × ℎ)

𝑆𝐴 = 2(12𝑖𝑛 × 2𝑖𝑛) + 2(12𝑖𝑛 × 3𝑖𝑛) + 2(2𝑖𝑛 × 3𝑖𝑛)

𝑆𝐴 = 2(24𝑖𝑛2) + 2(36𝑖𝑛2) + 2(6𝑖𝑛2)

𝑆𝐴 = 48𝑖𝑛2 + 72𝑖𝑛2 + 12𝑖𝑛2

𝑆𝐴 = 132𝑖𝑛2

Length

Width

Height

WE DO

YOU DO

𝑆𝐴 = 2(𝑙 × 𝑤) + 2(𝑙 × ℎ) + 2(𝑤 × ℎ)

𝑆𝐴 = 2(8𝑚 × 6𝑚) + 2(8𝑚 × 22𝑚) + 2(6𝑚 × 22𝑚)

𝑆𝐴 = 2(48𝑚2) + 2(176𝑚2) + 2(132𝑚2)

𝑆𝐴 = 96𝑚2 + 352𝑚2 + 264𝑚2

𝑆𝐴 = 712𝑚2

Length

Width

Height

𝑆𝐴 = 2(𝑙 × 𝑤) + 2(𝑙 × ℎ) + 2(𝑤 × ℎ)

𝑆𝐴 = 2(29𝑓𝑡 × 16𝑓𝑡) + 2(29𝑓𝑡 × 23𝑓𝑡) + 2(16𝑓𝑡 × 23𝑓𝑡)

𝑆𝐴 = 2(464𝑓𝑡2) + 2(667𝑓𝑡2) + 2(368𝑓𝑡2)

𝑆𝐴 = 928𝑓𝑡2 + 1334𝑓𝑡2 + 736𝑓𝑡2

𝑆𝐴 = 2998𝑓𝑡2

LengthWidth

Height

𝑆𝐴 = 2(𝑙 × 𝑤) + 2(𝑙 × ℎ) + 2(𝑤 × ℎ)

𝑆𝐴 = 2(4𝑐𝑚 × 1.2𝑐𝑚) + 2(4𝑐𝑚 × 2.8𝑐𝑚) + 2(1.2𝑐𝑚 × 2.8𝑐𝑚)

𝑆𝐴 = 2(4.8𝑐𝑚2) + 2(11.2𝑐𝑚2) + 2(3.36𝑐𝑚2)

𝑆𝐴 = 9.6𝑐𝑚2 + 22.4𝑐𝑚2 + 6.72𝑐𝑚2

𝑆𝐴 = 38.72𝑐𝑚2

Length

Width

Height